How complement maps can cure divergences


Paycha, S. (2019). How complement maps can cure divergences. Perimeter Institute. https://pirsa.org/19110085


Paycha, Sylvie. How complement maps can cure divergences. Perimeter Institute, Nov. 18, 2019, https://pirsa.org/19110085


          @misc{ pirsa_PIRSA:19110085,
            doi = {10.48660/19110085},
            url = {https://pirsa.org/19110085},
            author = {Paycha, Sylvie},
            keywords = {Quantum Fields and Strings, Quantum Gravity},
            language = {en},
            title = {How complement maps can cure divergences},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110085 see, \url{https://pirsa.org}}

Sylvie Paycha University of Potsdam


Complements offer a separating device which proves useful for renormalisation purposes. A set and its set complement are disjoint, a vector space and its orthogonal complement have trivial intersection. Inspired by J. Pommersheim and S. Garoufalidis, we define a class of complement maps which give rise to a class of binary relations that generalise the disjointness of sets and the orthogonality of vector spaces. We discuss how these reflect locality in quantum field theory and how they can be used for renormalisation purposes. This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang.